A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and rest from house E. Asingle student is selected at random to be the class monitor. The probability that theselected student is not from A, B and C is (A) $\frac{4}{23}$                 (B) $\frac{6}{23}$                   (C) $\frac{8}{23}$                   (D) $\frac{17}{23}$

Solution.  Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a
random event. The value is expressed from zero to one.
Total students = 23
Students in A, B, C = 4 + 8 + 5 = 17
Students in C, D = 23 – 17 = 6
Number of favourable cases = 6
Let A be the event that the student is not from A, B, C

$p\left ( A \right )= \frac{Student\, from\, C,D}{Total\, students}$

$p\left ( A \right )= \frac{6}{23}$